Another person checking in to say he's done all of these things. And it's really not that bad in most cases as people who have not done it seem to think.
First of all, most of those weather conditions are actually very rare. Even bike communiting every day in Canadian winter is not that bad in a city. Most roads are sufficiently poughed, that snowfall depth really is irrelvant (just make sure you have suitable bike tires). And you'd be surprised how warm you stay when cycling; it was often more of a problem for me being overheating than being too cold in the winter. That's why dressing with layers is key! So you can adjust...
Significant rain (at last where I am, which is pretty average) is usually not an issue. Rain comes and goes; shift your schedule slightly and watch local weather radar and you usually can find a relatively tame window to travel through. Days where it rains hard all day are relatively rare.
Other weather is mostly a matter of some simple gear. People would be amazed when I'd show up from a torrential downpour on my bike, get into the office and strip my rain pants, shoe covers, and rain jacket, gloves, wipe my glasses & face, and be 100% dry. It's no big deal; but just an alien concept to them. The people driving to work could be wetter than me! (Because they had to run from their car parking.... and where not equipped for the weather.)
Riding a bike year round makes you very intimate with weather, and it's not bad at all (usually). In fact it feels quite wonderful to have that connection with weather, and not be controlled by weather. I describe above staying completely dry biking in rain; but actually the other lesson you learn is that actually it's not so bad being wet either! You just go with it and learn not to worry about it...
Most of the people complaining about bikes never try it! Try it! It's great, and a whole new perspective. (Unless maybe your bike is exceptionally crappy.)